About: Gromov–Witten invariant

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In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten.

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rdf:type	plant
rdfs:label	Gromov–Witten invariant (en)
rdfs:comment	In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten. (en)
sameAs	Gromov–Witten invariant
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_web dbt:String_theory dbt:Algebraic_curves_navbox
Subject	Algebraic geometry String theory Symplectic topology Moduli theory
gold:hypernym	Numbers
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Gromov–Witten_invariant?oldid=1068171166&ns=0
Wikipage page ID	2301291 (xsd:integer)
page length (characters) of wiki page	12045 (xsd:nonNegativeInteger)
Wikipage revision ID	1068171166 (xsd:integer)
Link from a Wikipage to another Wikipage	Floer homology Algebraic geometry Almost complex manifold Atiyah–Bott fixed-point theorem Seiberg–Witten invariants Taubes's Gromov invariant Cambridge University Press Algebraic geometry String theory Symplectic topology General relativity Generating function Genus (mathematics) Donaldson theory Donaldson–Thomas theory Kuranishi structure Michael Atiyah Quantum cohomology Quantum mechanics Surjective function Chern class Cup product Linearization Pseudoholomorphic curve Clifford Taubes Closed manifold Cohomology Cokernel Cotangent complex Edward Witten Homology (mathematics) Orbifold Elementary particle Fundamental class Gopakumar–Vafa invariant Morphism of schemes Schubert calculus Symplectic geometry Calabi–Yau manifold Helmholtz free energy Intersection theory Invariant (mathematics) Kähler manifold Künneth theorem Mikhael Gromov (mathematician) Moduli of algebraic curves Moduli space Type II string theory Vector bundle Euler class Stable map Worldsheet Topological string theory Toric variety Path integral formulation Mathematics Measure (mathematics) Raoul Bott Rational number Moduli theory dbr:Arxiv:1110.6395 dbr:Arxiv:alg-geom/9608011
has abstract	In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten. The rigorous mathematical definition of Gromov–Witten invariants is lengthy and difficult, so it is treated separately in the stable map article. This article attempts a more intuitive explanation of what the invariants mean, how they are computed, and why they are important. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Gromov–Witten_invariant
is Wikipage redirect of	Gromov-Witten invariant Gromov–Witten invariants Relative Gromov–Witten invariant Relative Gromov-Witten invariant Gromov-Witten-invariants Gromov-Witten Invariant Gromov-Witten Invariants Gromov-Witten invariants Gromov-Witten theory Gromov witten Gromov–Witten theory
is Link from a Wikipage to another Wikipage of	Gromov-Witten invariant Gromov–Witten invariants List of unsolved problems in mathematics Mark Gross (mathematician) Algebraic curve Andrei Okounkov Behrend function Bernd Siebert

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